Relations and F...

Find $$g(x)$$, if $$f(x) = 7x + 12$$ and $$f(g(x) = 21x^{2} + 40$$

Given a function $$f(x) = \log_{7}\dfrac {x}{8}$$ for $$x\geq 8$$, find $$f^{-1}(x) $$, for $$x$$ belonging to its domain.

Given a function $$f(x) = \dfrac {1}{2}x - 4$$ and the composite function $$f(g(x)) = g(f(x))$$, determine which among the following can be $$g(x)$$:
I. $$2x - \dfrac {1}{4}$$
II. $$2x + 8$$
III. $$\dfrac {1}{2}x - 4$$

If $$f(x) = 4x - 3$$ and $$g(x) = x - 4$$, determine which of the following composite function has a value of $$-11$$.

The above figure shows the graph of the function $$f(x)$$, the value of $$f(f(3))$$ is:

$$*$$ is a binary operation on $$Z$$ such that:
$$a * b = a + b + ab$$.
The solution of $$(3* 4) *x = -1$$ is

Extraction of a cube root of a given number is

If $$f(x) = 3x - 5$$ and $$g(x) = x^2 + 1, f [g(x)] =$$

If $$f(x)=3x-1$$ and if $${f}^{-1}$$ is the inverse function of $$f$$, what is $${f}^{-1}(5)$$?

If $$a*b = |a-b|$$ then $$6*8$$ will be